Question: Express your answer as a mixed number simplified to lowest terms. $12\dfrac{7}{16}-8\dfrac{7}{12} = {?}$
Solution: Find a common denominator for the fractions: $= {12\dfrac{21}{48}}-{8\dfrac{28}{48}}$ Convert ${12\dfrac{21}{48}}$ to ${11 + \dfrac{48}{48} + \dfrac{21}{48}}$ So the problem becomes: ${11\dfrac{69}{48}}-{8\dfrac{28}{48}}$ Separate the whole numbers from the fractional parts: $= {11} + {\dfrac{69}{48}} - {8} - {\dfrac{28}{48}}$ Bring the whole numbers together and the fractions together: $= {11} - {8} + {\dfrac{69}{48}} - {\dfrac{28}{48}}$ Subtract the whole numbers: $=3 + {\dfrac{69}{48}} - {\dfrac{28}{48}}$ Subtract the fractions: $= 3+\dfrac{41}{48}$ Combine the whole and fractional parts into a mixed number: $= 3\dfrac{41}{48}$